Nonparametric approaches have recently emerged as a flexible way to model longitudinal data. This entry reviews some of the common nonparametric approaches to incorporate time and other covariate effects for longitudinally observed response data. Smoothing procedures are invoked to estimate the associated nonparametric functions, but the choice of smoothers can vary and is often subjective. Bot...

We consider testing whether the nonparametric function in a semiparametric additive mixed model is a simple fixed degree polynomial, for example, a simple linear function. This test provides a goodness-of-fit test for checking parametric models against nonparametric models. It is based on the mixed-model representation of the smoothing spline estimator of the nonparametric function and the vari...

Stochastic nonparametric envelopment of data (StoNED) combines the virtues of data envelopment analysis (DEA) and stochastic frontier analysis (SFA) into a unified framework of frontier estimation. StoNED melds the nonparametric piece-wise linear DEA-type frontier with stochastic SFA-type inefficiency and noise terms. We show that the StoNED model can be estimated in the panel data setting in a...

We consider a generalized regression model with a partially linear index. The index contains an additive nonparametric component in addition to the standard linear component, and the model’s dependent variable is transformed by a unknown monotone function. We propose weighted rank estimation procedures for estimating (i) the coe¢ cients for the linear component, (ii) the nonparametric component...

Wepropose amixedmultinomial logit model, with themixing distribution assigned a general (nonparametric) stick-breaking prior.Wepresent aMarkov chainMonte Carlo (MCMC) algorithm to sample and estimate the posterior distribution of the model’s parameters. The algorithm relies on a Gibbs (slice) sampler that is useful for Bayesian nonparametric (infinite-dimensional) models. The model and algorith...

Nonparametric estimation of a density from contaminated data is a difficult problem, for which convergence rates are notoriously slow. We introduce parametrically assisted nonparametric estimators which can dramatically improve on performance of standard nonparametric estimators when the assumed model is close to the true density, without degrading much the quality of purely nonparametric estim...